Question

Let A,B, and C be events relating to the experiment of rolling a pair of dice.
(a) If
P(A|C) > P(B|C) and P(A|Cc) > P(B|Cc)
either prove that P(A) > P(B) or give a counterexample by defining events A,B, and C for which that relationship is not true.
(b) If
P(A|C) > P(A|Cc) and P(B|C) > P(B|Cc)
either prove that P(AB|C) > P(AB|Cc) or give a counterexample by defining events A,B, and C for which that relationship is not true.
Let C be the event that the sum of a pair of dice is 10; let A be the event that the first die lands on 6; let B be the event that the second die lands on 6.